 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/2/b/ii/solution

A pair belongs to

R \circ R

exactly when two successive

R

steps connect its endpoints. The chain

a \to b \to c \to d

has two such length-two paths,

a \to b \to c

and

b \to c \to d

. Hence

R \circ R = {(a, c), (b, d)} .

This applies composition of relations directly; no other middle element gives a pair.

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